The Arithmetic of Elliptic Curves:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
New York, NY
Springer New York
1986
|
| Schriftenreihe: | Graduate Texts in Mathematics
106 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | The preface to a textbook frequently contains the author's justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently being done in this area, the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Kob]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5J, which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts. Our approach is more algebraic than that taken in, say, [La 3] or [La 5], where many of the basic theorems are derived using complex analytic methods and the Lefschetz principle. For this reason, we have had to rely somewhat more on techniques from algebraic geometry. However, the geom etry of (smooth) curves, which is essentially all that we use, does not require a great deal of machinery |
| Beschreibung: | 1 Online-Ressource (XII, 402 p) |
| ISBN: | 9781475719208 9781475719222 |
| ISSN: | 0072-5285 |
| DOI: | 10.1007/978-1-4757-1920-8 |
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| 500 | |a The preface to a textbook frequently contains the author's justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently being done in this area, the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Kob]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5J, which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts. Our approach is more algebraic than that taken in, say, [La 3] or [La 5], where many of the basic theorems are derived using complex analytic methods and the Lefschetz principle. For this reason, we have had to rely somewhat more on techniques from algebraic geometry. However, the geom etry of (smooth) curves, which is essentially all that we use, does not require a great deal of machinery | ||
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Datensatz im Suchindex
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|---|---|
| any_adam_object | |
| author | Silverman, Joseph H. |
| author_facet | Silverman, Joseph H. |
| author_role | aut |
| author_sort | Silverman, Joseph H. |
| author_variant | j h s jh jhs |
| building | Verbundindex |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 512 - Algebra |
| dewey-raw | 512 |
| dewey-search | 512 |
| dewey-sort | 3512 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4757-1920-8 |
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| id | DE-604.BV042421296 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:08Z |
| institution | BVB |
| isbn | 9781475719208 9781475719222 |
| issn | 0072-5285 |
| language | English |
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| spelling | Silverman, Joseph H. Verfasser aut The Arithmetic of Elliptic Curves by Joseph H. Silverman New York, NY Springer New York 1986 1 Online-Ressource (XII, 402 p) txt rdacontent c rdamedia cr rdacarrier Graduate Texts in Mathematics 106 0072-5285 The preface to a textbook frequently contains the author's justification for offering the public "another book" on the given subject. For our chosen topic, the arithmetic of elliptic curves, there is little need for such an apologia. Considering the vast amount of research currently being done in this area, the paucity of introductory texts is somewhat surprising. Parts of the theory are contained in various books of Lang (especially [La 3] and [La 5]); and there are books of Koblitz ([Kob]) and Robert ([Rob], now out of print) which concentrate mostly on the analytic and modular theory. In addition, survey articles have been written by Cassels ([Ca 7], really a short book) and Tate ([Ta 5J, which is beautifully written, but includes no proofs). Thus the author hopes that this volume will fill a real need, both for the serious student who wishes to learn the basic facts about the arithmetic of elliptic curves; and for the research mathematician who needs a reference source for those same basic facts. Our approach is more algebraic than that taken in, say, [La 3] or [La 5], where many of the basic theorems are derived using complex analytic methods and the Lefschetz principle. For this reason, we have had to rely somewhat more on techniques from algebraic geometry. However, the geom etry of (smooth) curves, which is essentially all that we use, does not require a great deal of machinery Mathematics Algebra Number theory Number Theory Mathematik Diophantische Approximation (DE-588)4135760-7 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 gnd rswk-swf Algebraische Varietät (DE-588)4581715-7 gnd rswk-swf Algebraische Zahlentheorie (DE-588)4001170-7 gnd rswk-swf Algebra (DE-588)4001156-2 gnd rswk-swf Elliptische Kurve (DE-588)4014487-2 s Algebra (DE-588)4001156-2 s Algebraische Zahlentheorie (DE-588)4001170-7 s 1\p DE-604 Diophantische Approximation (DE-588)4135760-7 s 2\p DE-604 Algebraische Varietät (DE-588)4581715-7 s 3\p DE-604 https://doi.org/10.1007/978-1-4757-1920-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 3\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Silverman, Joseph H. The Arithmetic of Elliptic Curves Mathematics Algebra Number theory Number Theory Mathematik Diophantische Approximation (DE-588)4135760-7 gnd Elliptische Kurve (DE-588)4014487-2 gnd Algebraische Varietät (DE-588)4581715-7 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Algebra (DE-588)4001156-2 gnd |
| subject_GND | (DE-588)4135760-7 (DE-588)4014487-2 (DE-588)4581715-7 (DE-588)4001170-7 (DE-588)4001156-2 |
| title | The Arithmetic of Elliptic Curves |
| title_auth | The Arithmetic of Elliptic Curves |
| title_exact_search | The Arithmetic of Elliptic Curves |
| title_full | The Arithmetic of Elliptic Curves by Joseph H. Silverman |
| title_fullStr | The Arithmetic of Elliptic Curves by Joseph H. Silverman |
| title_full_unstemmed | The Arithmetic of Elliptic Curves by Joseph H. Silverman |
| title_short | The Arithmetic of Elliptic Curves |
| title_sort | the arithmetic of elliptic curves |
| topic | Mathematics Algebra Number theory Number Theory Mathematik Diophantische Approximation (DE-588)4135760-7 gnd Elliptische Kurve (DE-588)4014487-2 gnd Algebraische Varietät (DE-588)4581715-7 gnd Algebraische Zahlentheorie (DE-588)4001170-7 gnd Algebra (DE-588)4001156-2 gnd |
| topic_facet | Mathematics Algebra Number theory Number Theory Mathematik Diophantische Approximation Elliptische Kurve Algebraische Varietät Algebraische Zahlentheorie |
| url | https://doi.org/10.1007/978-1-4757-1920-8 |
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